Measurements of the Decays ${\tau }^{-}\to h^{-}{h}^{+}{h}^{-}{\nu }_{\tau }$ and ${\tau }^{-}\to h^{-}{h}^{+}{h}^{-}{\pi }^0{\nu }_{\tau }$

We use a data sample of 2.8 × ${10}^6$ produced $\tau$-pair events, obtained with the CLEO II detector, to measure $\mathcal{B}({\tau }^{-}\to h^{-}{h}^{+}{h}^{-}({\pi }^0\left){\nu }_{\tau }\right)$, where $h$ refers to either a charged $\pi$ or $K$. These branching fractions are measured with samples of lepton-tagged and 3 vs 3 events. We find $\mathcal{B}({\tau }^{-}\to h^{-}{h}^{+}{h}^{-}{\nu }_{\tau })=0.0951\mathrm{}\pm 0.0007\pm 0.0020$ and $\mathcal{B}({\tau }^{-}\to h^{-}{h}^{+}{h}^{-}{\pi }^0{\nu }_{\tau })=0.0423\mathrm{}\pm 0.0006\pm 0.0022$. We also measure $\mathcal{B}({\tau }^{-}\to \omega h^{-}{\nu }_{\tau })=0.0195\mathrm{}\pm 0.0007\pm 0.0011$.